The present invention relates to an apparatus for determining the concentration of a light-absorbing material in blood.
An oximeter is an example of an apparatus currently employed to determine the concentration of light-absorbing materials in blood. In a known type of oximeter, the oxygen saturation of blood in a living tissue sample is computer based on the fact that the relative quantities of two light beams having different wavelengths that pass through the tissue sample differ on account of blood pulsation. The operating principle of this type of oximeter is described hereinafter.
It is assumed first that a living tissue sample through which light is to pass is composed of a blood containing tissue layer and non-blood tissue layer as shown in FIG. 1A. In this case, the light attentuation by the overall tissue sample is expressed by: EQU -log (I.sub.1 /I.sub.0)=A+B (1)
where
I.sub.0 : the quantity of incident light, PA1 I.sub.1 : the quantity of transmitted light, PA1 A: the amount of light attenuation by the non-blood containing tissue, and PA1 B: the amount of light attenuation by the blood containing layer. PA1 E: the absorptivity coefficient of hemoglobin, PA1 C: the concentration of hemoglobin in blood, and PA1 D: the thickness of the blood layer.
The light attenuation by the blood layer (B) is expressed by: EQU B=E.multidot.C.multidot.D (2)
where
Therefore, equation (1) can be rewritten as: EQU -log (I.sub.1 /I.sub.0)=A+E.multidot.C.multidot.D (3)
The thickness of the blood layer D is variable due the normal arteiral blood pulsating. It is assumed that the thickness of the blood layer changes by .DELTA.D as shown in FIG. 1B. If the quantity of light transmitted through the blood layer changed in thickness by .DELTA.D is written as I.sub.2, analogy with equation (3) gives: EQU -log (I.sub.2 /I.sub.0)=A+E.multidot.C.multidot.(D+.DELTA.D) (4)
Subtracting equation (4) from equation (3), EQU -{log (I.sub.1 /I.sub.0)-log (I.sub.2 /I.sub.0)}=-EC.DELTA.D, EQU or EQU -log (I.sub.2 /I.sub.1)=EC.DELTA.D (5)
As can be seen from equation (3), equation (5) is equivalent to the expression of light attenuation for the case where incident light having an intensity of I.sub.1 passes through a blood containing layer with a thickness of .DELTA.D to produce light transmission in a quantity I.sub.2. This relation is depicted in FIG. 1C.
Next will be considered the case where two light beams having different wavelengthsare transmitted through a blood containing layer at the measurement site. FIG. 2 shows the relationship between the thickness of the blood containing layer D and each of I.sub.1 (the quantity of transmitted light at a wavelength of .lambda..sub.1) and I.sub.2 (the quantity of transmitted light having a wavelength of .lambda..sub.2). If the change in the thickness of the blood layer that occurs between two points in time t.sub.1 and t.sub.2 is written as .DELTA.D, and if the values of I.sub.1 and I.sub.2 at time t.sub.1 are written as I.sub.11 and I.sub.12, respectively, with the values of I1 and I2 at time t.sub.2 being written as I.sub.21 and I.sub.22, respectively, the following relations are established in consideration of equation (5):
For the first wavelength .lambda..sub.1 : EQU -log (I.sub.21 /I.sub.11)=E.sub.1 C.DELTA.D (6)
For the second wavelength .lambda..sub.2 : EQU -log (I.sub.22 /I.sub.12)=E.sub.2 C.DELTA.D (7)
where E.sub.1 is the absorptivity coefficient of the blood for light at the wavelength .lambda..sub.1 and E.sub.2 is the absorptivity coefficient of the blood for light at the wavelength .lambda..sub.2.
Equations (6) and (7) can be rewritten as follows: EQU log (I.sub.11 /I.sub.21)=E.sub.1 C.DELTA.D (8) EQU log (I.sub.12 /I.sub.22)=E.sub.2 C.DELTA.D (9)
Dividing equation (9) by equation (8) and writing the quotient as .phi., EQU .phi.={log (I.sub.12 /I.sub.22)}/{log (I.sub.11 /I.sub.21)}=E.sub.1 /E.sub.2 ( 10)
Since equation (10) does not contain the term .DELTA.D, the times t.sub.1 and t.sub.2 may be any two values.
Equation (10) can be rewritten as; EQU E.sub.2 =.phi..multidot.E.sub.1 ( 11)
If the absorptivity coefficient E.sub.1 in equation (11) is known, E.sub.2 can be determined by calculating .phi.. As equation (10) shows, .phi.can be determined by calculating log (I.sub.11 /I.sub.21) and log (I.sub.12 /I.sub.22), and as already mentioned, log (I.sub.11 /I.sub.21) can be determined by measuring I.sub.11 and I.sub.21 (the quantities of transmitted light at the wavelength .lambda..sub.1 at any two points in time), while log (I.sub.12 /I.sub.22) can be determined by measuring I.sub.12 and I.sub.22 (the quantities of transmitted light at the wavelength .lambda..sub.2 at the aforementioned any two points in time).
Since EQU log (I.sub.11 /I.sub.21)=log I.sub.11 -log I.sub.21 ( 12) EQU log (I.sub.12 /I.sub.22)=log I.sub.12 -log I.sub.22 ( 13)
the logarithm of I.sub.21 may be subtracted from the logarithm of I.sub.11 to obtain log (I.sub.11 /I.sub.21) while the logarithm of I.sub.22 is subtracted from the logarithm of I.sub.12 to obtain log (I.sub.12 /I.sub.22).
Equation (12) can be rewritten as log (I.sub.11 /I.sub.21)=log {1+(I.sub.11 -I.sub.21)/I.sub.21 }. Since I.sub.11 -I.sub.21, the following approximation is valid: EQU log (I.sub.11 /I.sub.21)=(I.sub.11 -I.sub.21)/I.sub.21 ( 14)
In like manner, the following approximation is valid: EQU log (I.sub.12 /I.sub.22)=(I.sub.22 -I.sub.22)/I.sub.22 ( 15)
Using E.sub.2, the oxygen saturation S of blood may be calculated by the following procedures.
The absorptivity coefficient E of the blood versus the wavelength .lambda. of light with which a living body is irradiated is shown in FIG. 3 for S=0% and S=100%. The wavelength at which the curve for S=0% crosses the curve for S=100% is selected as the first wavelength .lambda..sub.1, which falls at 805 nm in FIG. 3. The absorptivity coefficient E.sub.1 for the light beam having the wavelength .lambda..sub.1 is insensitive to changes in the oxygen saturation of blood S. Accordingly, a wavelength different from .lambda..sub.1 is selected as the second wavelength .lambda..sub.2, which falls, for instance, at 660 nm in FIG. 3. At the wavelength .lambda..sub.2, the absorptivity coefficient assumes the value E.sub.r when S=0% and the value E.sub.0 if S=100%. E.sub.2 is a value between E.sub.0 and E.sub.r. Using E.sub.r, E.sub.0 and E.sub.2, S can be calculated by the following equation: EQU S=(E.sub.2 -E.sub.r)/(E.sub.0 -E.sub.r) (16)
An apparatus which determines the oxygen saturation S of blood using the procedure described above is shown schematically in FIG. 4. Detectors 1 and 2 receive light beams that have passed through a living tissue sample and which have wavelengths of .lambda..sub.1 and .lambda..sub.2, respectively, and produce output signals indicative of the intensities of the two beams. Variation computing circuits 3 and 4 compute the respective amounts of light attenuation on the basis of the changes in the detection signals produced by detectors 1 and 2 at two identical points in time. In other words, using I.sub.11 and I.sub.12 representing the quantities of transmitted light at time t.sub.1, as well as I.sub.21 and I.sub.22 representing the quantities of transmitted light at time t.sub.2 (see FIG. 2), the circuits 3 and 4 compute log (I.sub.11 /I.sub.21) and log (I.sub.12 /I.sub.22), respectively, which are the left side of equations (8) and (9). As a result, the variation in light attenuation due to the change in blood thickness (.DELTA.D) on the right side of each of equations (8) and (9) is determined. Using the calculation results produced by the circuits 3 and 4, a divider circuit 5 determines .phi. expressed by equation (10). In the next step, an oxygen saturation computing circuit 6 computes S from equations (11) and (12) using the value of .phi. calculated by the divider cirucit 5 and the preliminary stored values of E.sub.1, E.sub.r and E.sub.0 as indicated in FIG. 3.
The apparatus described above has the disadvantage that noise is unavoidably present in the signals produced by the detectors 1 and 2. Therefore, a single sampling will not yield a reliable value and the values obtained over several samplings must be averaged. However, the sampling for a single measurement can only be performed a finite number of times since the oxygen saturation of blood varies constantly. Furthermore, the two sets of data I.sub.11 and I.sub.12 and data I.sub.21 and I.sub.22 employed for the calculation by the variation computing circuits 3 and 4 are values obtained at any two respective arbitrary points in time t.sub.1 and t.sub.2, as shown in FIG. 2, and hence it sometimes occurs that the difference between I.sub.11 and I.sub.21 or between I.sub.12 and I.sub.22 is very small. If this happens, computation using the two sets of data I.sub.11 and I.sub.12 and data I.sub.21 and I.sub.22 will not produce highly precise results.